On topological properties of manifolds of eigenfunctions generated by a family of periodic Sturm–Liouville problems

In the paper, we study manifolds of eigenfunctions of a fixed oscillation. Then, solving the trivial inverse problem of reconstruction of a potential by an eigenfunction, we describe the properties of manifolds of potentials. The approach proposed allows one to link topological properties of manifolds of eigenfunctions with those of manifolds of potentials.